From Wikipedia, the free encyclopedia

Linear motion is motion along a straight line, and can therefore be described
mathematically using only one spatial dimension. It can be uniform, that is, with
constant velocity (zero
acceleration), or non-uniform, that is, with a variable velocity
(non-zero acceleration). The motion of a particle (a point-like
object) along the line can be described by its position x,
which varies with t (time).

An example of linear motion is that of a ball thrown straight up
and falling back straight down.

The average velocity v during a finite time span of a
particle undergoing linear motion is equal to

The instantaneous velocity of a particle in linear motion may be
found by differentiating the position x with
respect to the time variable t. The acceleration may be
found by differentiating the velocity. By the fundamental theorem of
calculus the converse is also true: to find the velocity when
given the acceleration, simply integrate the acceleration with respect to
time; to find displacement, simply integrate the velocity with
respect to time.

This can be demonstrated graphically. The gradient of a line on the displacement time graph
represents the velocity. The gradient of the velocity time graph
gives the acceleration while the area under the velocity time graph
gives the displacement. The area under an acceleration time graph
gives the velocity.

Linear motion is the most basic of all motions. According to Newton's
first law of motion, objects not subjected to forces will
continue to move uniformly in a straight line indefinitely. Under
every-day circumstances, external forces such as gravity and
friction will cause objects to deviate from linear motion and can
cause them to come to a rest.

For linear motion embedded in a higher-dimensional space, the
velocity and acceleration should be described as vectors, made up of two parts: magnitude
and direction. The direction part of these vectors is the same and
is constant for linear motion, and only for linear motion.